1. Field of the Invention
This invention relates to an optical proximity effect correcting method in photolithography, and more particularly to a mask pattern correcting method, which is applied to light exposure using, for example, an exposure device that meets NA>1.
2. Description of the Related Art
When the size of a pattern is larger than the exposure wavelength, a shape can be formed easily on a substrate as designed. Specifically, first, a planar shape of an LSI pattern to be formed on a substrate is drawn directly as a design pattern. Then, a mask pattern faithful to the design pattern is created. Thereafter, the mask pattern is transferred onto a substrate with a projection optical system and the underlying layer is etched, which produces a pattern almost as designed.
However, as the pattern has been miniaturized further, it has been getting difficult to form a pattern shape in faithful accordance with the mask pattern. A disorder in the faithfulness appears as a dimensional difference (roughness dimensional difference) between a region where the pattern period is short (dense region) and a region where the pattern period is long (isolated region). Generally, what is caused by light is referred to as an optical proximity effect (OPE) and what is caused by such a process as development or etching, in addition to light, is all referred to as a process proximity effect (PPE).
To solve an OPE or PPE problem, it is necessary to use a mask pattern differing from the design pattern and make the final finished dimensions and shape equal to the dimensions and shape of the design pattern. That is, a so-called mask data process to create a corrected mask pattern is important.
The mask data process includes an MDP process of changing the shape of the mask pattern using a graphic computation process, a design rule checker (DRC), or the like and an OPC process of correcting the OPE. These processes are performed, thereby correcting the mask pattern suitably so that the final finished dimensions may satisfy the desired requirements. To execute an OPC (optical proximity correction) process with a high accuracy, a model-based OPC method becomes mainstream which calculates a suitable shape correction value for each mask pattern using an optical image intensity simulator capable of accurately predicting the OPE caused by the characteristic of the optical system of the exposure device. The optical image intensity simulator has generally calculated the diffraction of light using a so-called thin-film mask model (also referred to as a Kirchhoff model), approximately considering the pattern of a mask to be not only a two-dimensional object with no thickness but also an ideal object characterized by the transmittance and phase error independent on the incident angle of light.
With the recent development of an immersion exposure device, a device whose projection lens NA exceeds 1 has been developed. Generally, the magnification of a projection lens is kept at ¼ as in the conventional equivalent, thereby trying to realize the miniaturization of the pattern, while keeping the same exposure area as the conventional one.
However, if the magnification of the projection lens is kept, for example, when a pattern with a half pitch of 45 nm is formed with an ArF exposure device (with an exposure wavelength of 193 nm), the half pitch on the mask is 45×4=180 nm. This means that the pattern dimensions on the mask are smaller than the exposure wavelength.
Under such a condition, the thin-film mask model is not a suitable approximation and it is necessary to do a numeric calculation using a Maxwell equation to predict the diffraction of light caused by a mask pattern (e.g., refer to Jpn. Pat. Appln. KOKAI Publication No. 2006-276260). The numeric calculation method includes, for example, a finite domain time difference method (FDTD method) and a rigorous coupled wave analytic method (RCWA method) written in T. V. Pistor, “Accuracy Issues in the Finite Difference Time Domain Simulation of Photomask Scattering,” Proc. SPIE Vol. 4346, pp. 1484-1491. In those numeric calculation methods, the thickness of the mask, the incident angle of light, and the optical constants of the object (refractive index and attenuation coefficient) are taken into account. Hereinafter, this is referred to as a 3D mask model in comparison with the thin-film mask model. When the dimensions of the pattern are sufficiently large, the 3D mask model brings the same result as that of the thin-film mask model.
The image intensity is simulated using a computer. The simulation of the image intensity requires a large capacity of memory to calculate a 3D mask model and takes more than a hundred times the time required to calculate a thin-film mask. Therefore, it is not realistic to predict the image density of the entire region of the mask pattern using a 3D mask model.
EUV exposure devices recently developed have an exposure wavelength as short as 13.5 nm. EUV exposure devices used in general have a projection lens whose magnification is ¼, and the value of NA is not more than 1, e.g., 0.25 or so. Although the size of the mask pattern is greater than the wavelength, the use of a reflection type mask inevitably requires oblique illumination, wherein light incident on a mask is inclined 6 to 10 degrees. In this case as well, the influence due to the thickness of the mask pattern is not negligible, so that there may be a case where the use of a 3D mask model is desirable.